# Frequency Diffeomorphisms for Efficient Image Registration

@article{Zhang2017FrequencyDF, title={Frequency Diffeomorphisms for Efficient Image Registration}, author={Miaomiao Zhang and Ruizhi Liao and Adrian V. Dalca and Esra Abaci Turk and Jie Luo and Patricia Ellen Grant and Polina Golland}, journal={Information processing in medical imaging : proceedings of the ... conference}, year={2017}, volume={10265}, pages={ 559-570 } }

This paper presents an efficient algorithm for large deformation diffeomorphic metric mapping (LDDMM) with geodesic shooting for image registration. We introduce a novel finite dimensional Fourier representation of diffeomorphic deformations based on the key fact that the high frequency components of a diffeomorphism remain stationary throughout the integration process when computing the deformation associated with smooth velocity fields. We show that manipulating high dimensional…

## 37 Citations

Fast Diffeomorphic Image Registration via Fourier-Approximated Lie Algebras

- MathematicsInternational Journal of Computer Vision
- 2018

This paper introduces Fourier-approximated Lie algebras for shooting (FLASH), a fast geodesic shooting algorithm for diffeomorphic image registration that approximate the infinite-dimensional Lie algebra of smooth vector fields with a low-dimensional, bandlimited space.

Efficient Laplace Approximation for Bayesian Registration Uncertainty Quantification

- Computer ScienceMICCAI
- 2018

A Laplace approximation of Bayesian registration models entirely in a bandlimited space that fully describes the properties of diffeomorphic transformations and dramatically reduces the computational complexity of approximating posterior marginals in the high dimensional imaging space.

Registration Uncertainty Quantification Via Low-dimensional Characterization of Geometric Deformations.

- Computer ScienceMagnetic resonance imaging
- 2019

Data-Driven Model Order Reduction for Diffeomorphic Image Registration

- Computer ScienceIPMI
- 2019

A reduced order model (ROM) is introduced to substantially lower the overall computational cost while maintaining accurate alignment in the context of large deformation diffeomorphic metric mapping (LDDMM) and is demonstrated in neuroimaging applications of pairwise image registration and template estimation for population studies.

Deep Learning for Regularization Prediction in Diffeomorphic Image Registration

- Computer ScienceArXiv
- 2020

A predictive model based on deep convolutional neural networks that learns the mapping between pairwise images and the regularization parameter of image registration and demonstrates the effectiveness of the model on both 2D synthetic data and 3D real brain images.

Diffeomorphic Image Registration with Neural Velocity Field

- Computer Science
- 2022

This paper proposes a neural representation of continuous velocity field (NeVF) to describe the deformations across two images that has higher flexibility in modeling the complex deformation field and proposes a simple sparse-sampling strategy to reduce the memory consumption.

Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration

- Computer ScienceMICCAI
- 2018

This paper presents a probabilistic generative model and derive an unsupervised learning-based inference algorithm that makes use of recent developments in convolutional neural networks (CNNs) and results in state of the art accuracy and very fast runtimes, while providing diffeomorphic guarantees and uncertainty estimates.

Band-Limited Stokes Large Deformation Diffeomorphic Metric Mapping

- Computer ScienceIEEE Journal of Biomedical and Health Informatics
- 2019

This paper proposes a novel method for efficient Stokes-LDDMM diffeomorphic registration that poses the constrained variational problem in the space of band-limited vector fields and it is implemented in the GPU.

Unsupervised Learning of Probabilistic Diffeomorphic Registration for Images and Surfaces

- Computer ScienceMedical Image Anal.
- 2019

CycleMorph: Cycle Consistent Unsupervised Deformable Image Registration

- Computer ScienceMedical Image Anal.
- 2021

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